Abstract

This paper presents a dynamical and computational model for the analysis of the interaction of a flexible Euler-Bernoulli beam attached to a uniformly rotating hub, and a flat rigid surface, parallel to the axis of the hub. The dynamic model is derived using Lagrange’s equations in conjunction with an eigenfunctions-generalized-coordinates based representation of the displacement fields. It is shown that one must account for the longitudinal displacements if dynamical stiffening is to be observed. A quadratic approximation for these displacements is used and a computationally effective way of by-passing the calculation of the volume integrals at every integration step, by matrix-vector multiplications is implemented. The energy dissipating constraint, which requires the tip of the filament to move on the surface is imposed with a Lagrange multiplier and a generalized friction force. A procedure of evaluating the generalized friction force in terms of the generalized coordinates and velocities is presented. A complete numerical algorithm for the entire intermittent interaction process is developed. The presence of dynamical stiffening is tested and the calculated values of the fundamental frequency are found in excellent agreement with data from literature. Simulation results for the time history of the normal contact force indicate that the contact zone is discontinuous, and that the force is strongly dependent on the hub angular speed and on the distance from the center to the flat surface.

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